The radial distribution function provides an intuitive link between microscopic structure and macroscopic behavior. By describing how the probability of finding a neighboring particle varies with distance, it reveals characteristic length scales, local ordering, and phase structure. Combined with intermolecular potentials and statistical-mechanical relations, it also provides access to thermodynamic and transport properties, including internal energy, pressure, chemical potential, viscosity, among others. This lecture extends this familiar number-based description to volume- and surface-based pair-correlation functions for agglomerates of nanoparticles through a unified framework. This distinction is important because nanoparticles are not point objects: their finite dimensions, interfaces, and organization determine how they scatter radiation and interact with surrounding matter. We will examine how the three correlations emphasize complementary aspects of the same structure, from particle-center organization to the spatial distributions of matter and accessible surface area. The lecture will then develop two physical applications. First, we will connect real-space correlations to the structure factor which could be measured through X-ray, neutron, and light scattering, showing how fractal scaling and primary-particle structure appear across different ranges of scattering vector. Second, we will show how pair correlations can be combined with microscopic interaction potentials to approximate van der Waals interactions involving complex fractal-like agglomerates. These interactions govern processes such as coagulation, adhesion, filtration, impaction, restructuring, and resuspension. Throughout, emphasis will be placed on physical interpretation, characteristic scales, and how selecting an appropriate correlation measure enables predictions of experimentally observable properties and collective particle behavior.
José Morán received a BSc and an MSc in engineering from the Universidad Técnica Federico Santa Maria in Chile, both in 2017. In 2021, he received a PhD in Physics at INSA de Rouen in France, conducting research in the CORIA laboratory. He also conducted postdoctoral research for several months at Carleton University, Canada, and at the University of Minnesota, U.S., for two years. He joined the University of Ottawa’s Department of Mechanical Engineering as an assistant professor in July 2024.